Customary planing machines, and particularly hand-held planers, use rotary cutters in which cutter blades are located on a cylindrical cutting element which is driven by an electric motor to rotate in a direction essentially transverse to the longitudinal extent of the machine. The cutter is operative within an operating or working chamber which is open at the planing surface to project slightly from the planing surface and thereby effect workpiece removal upon rotation. The opening at the planing surface is wider than the cutter to permit removal of workpiece material in chip form through a portion of the housing for ejection therefrom, usually in a lateral direction. The cutting edges of the planer, as they rotate, cause recurrent pressure wave to occur which arise at the edges of the respective housing portions defining the operating chamber. Since the cutter operates at high speed, the sharp, pulse-like pressure waves cause substantial operating noise which is highly disagreeable to the user and causes, overall, ambient noise pollution.